Possible Sets of A's in a Class of 30 Students

In summary, the first part of the conversation discusses assigning grades to 30 students in a class with 5 receiving A's, 20 receiving B's, and the remainder receiving C's. The second part involves determining the probability of selecting a group of 5 students at random and none of them being assigned an A. The solution involves calculating the number of sets of 5 students not receiving an A and dividing it by the total number of sets of 5 students.
  • #1
Ronnin
168
1
This one seems simple, but I want to be sure I'm using the correct thinking.

Homework Statement



If there are 30 students in a class and 5 of them are to be assigned A's, 20 to be assigned B's, and the remainder C's, how many different sets of students receiving A's are possible?


2nd Part

Determine the probability of a group of 5 students being selected at random and none of the 5 being assigned an A.

Homework Equations


None


The Attempt at a Solution


Would this be just a 30 choose 5 question since there are 5 students who can make an A out of 30?
 
Last edited:
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  • #2
Ronnin said:

The Attempt at a Solution


Would this be just a 30 choose 5 question since there are 5 students who can make an A out of 30?

For the first part.
The second part is a bit more involved.
 
  • #3
I hate to ask, but any idea of how I should start with the second part?
 
  • #4
Now you need to find out how many sets of 5 students not receiving an A are possible. This is not the final solution but it gets you started...
 
  • #5
Maybe it well help to give you a similar problem. Say you have ten pens and two are broken. How many sets of one member are there of broken pens? Well, two, because there are two broken pens. How many sets of one member are there of functioning pens? Eight. Now...how many sets of two are there of broken pens? One. How many sets of two are there of working pens?
 
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  • #6
Rashad9607 said:
Maybe it well help to give you a similar problem. Say you have ten pens and two are broken. How many sets of one member are there of broken pens? Well, two, because there are two broken pens. How many sets of one member are there of functioning pens? Eight. Now...how many sets of two are there of broken pens? One. How many sets of two are there of working pens?

Wouldn't it be nCr=28?
 
  • #7
Would the prob be 30 choose 25 for the prob of not choosing a student with an A, 142506?
 
  • #8
Ronnin said:
Would the prob be 30 choose 25 for the prob of not choosing a student with an A, 142506?

No, a probability will never be greater than 1. You need to calculate the number of ways to choose 5 students from the group of other than A students. Then divide that number by the number of ways to choose 5 students from the entire group.

You have 25 students that did not get an A. Choose 5.

You have 30 students total. Choose 5.

This is close to the complete solution...
 

What is simple probability?

Simple probability refers to the likelihood or chance of a single event occurring. It is calculated by dividing the number of desired outcomes by the total number of possible outcomes.

How do you calculate simple probability?

To calculate simple probability, divide the number of desired outcomes by the total number of possible outcomes. For example, if you are rolling a six-sided die and want to know the probability of rolling a 3, the calculation would be 1 desired outcome (rolling a 3) divided by 6 possible outcomes (rolling any number from 1 to 6), resulting in a probability of 1/6 or 16.67%.

What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data collected from experiments or observations and may differ from theoretical probability due to chance or other factors.

Can simple probability be greater than 1?

No, simple probability cannot be greater than 1. This would indicate that the event is certain to occur, which is not possible. The maximum value for simple probability is 1, which represents a 100% chance of the event occurring.

How does simple probability relate to real-life situations?

Simple probability can be used to make predictions and decisions in real-life situations. For example, a weather forecast predicting a 60% chance of rain is using simple probability to estimate the likelihood of rain occurring. In gambling, understanding simple probability can help players make informed decisions about their bets. It is also used in fields such as medicine, finance, and sports to analyze and assess risks and outcomes.

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